\usepackage{amsthm}
% 定理命题
\theoremstyle{plain}
\newtheorem{thm}{\protect\theoremname}
\newtheorem{cor}{\protect\corollaryname}
\newtheorem{lem}{\protect\lemmaname}
\newtheorem{proposition}{\protect\propositionname}

\theoremstyle{definition}
\newtheorem{defenv}{\protect\definitionname}
\newtheorem{example}{\protect\examplename}
\newtheorem{fact}{\protect\factname}

\theoremstyle{remark}
\newtheorem{rem}{\protect\remarkname}
\newtheorem{note}{\protect\notename}


\providecommand{\theoremname}{定理}
\providecommand{\corollaryname}{推论}
\providecommand{\lemmaname}{引理}
\providecommand{\propositioname}{命题}
\providecommand{\definitionname}{定义}
\providecommand{\examplename}{示例}
\providecommand{\factname}{事实}
\providecommand{\remarkname}{注释}
\providecommand{\notename}{笔记}